Abstract
The plasma-redshift cross-section is a newly discovered interaction of photons with hot sparse
plasma. This cross section is derived from conventional physics by more exact calculations
than those conventionally used to derive the cross section for photo-electric effect, Compton
scattering, and the Raman scattering. This new plasma-redshift cross-section explains the
redshift of the solar Fraunhofer lines, the intrinsic redshifts of stars, quasars, and galaxies, the
cosmological redshift, the magnitude-redshift relation for supernovae Ia (SNe Ia), the cosmic
microwave background (CMB), the cosmic X-ray background, and the surface brightness of
galaxies. There is no need for dark energy, dark matter, or black holes. In this article we
show that plasma-redshift cosmology leads to hot quark-gluon plasma at the centers of black
hole candidates and super-massive black hole candidates. The conditions are similar to those
surmised ad hoc in the initial phases of the Big Bang. Plasma-redshift cosmology thus explains
eternal renewal of matter and primordial like nucleosynthesis. We have failed to find any need
or reasonable support for the Big Bang. We find that the observed nucleosynthesis and the
many other phenomena are consistent with the plasma-redshift cosmology.

Many assume that the predictions of the Big Bang model compare well with the observed concentration of the light elements; see Peebles’ monograph [1]; see also Schramm [2] who states: ”The
bottom line remains: primordial nucleosynthesis has joined the Hubble expansion and the microwave
background radiation as one of the three pillars of Big Bang cosmology”. However, others find large
discrepancies between the observations and the predictions. Quoting Thomas et al. Rollinde et
al. [3] find that: ”In effect, we are faced with explaining a 6 Li plateau at a level of about 1000 times
that expected from BBN”. Thus it appears that the observed values of the elements often deviate
from the predicted values; and it has been difficult or not possible to explain these deviations.
Spergel (see section 11.2.3 of [4]) finds that: The ”observations appear to require either a significant modification of our ideas about Big Bang nucleosynthesis or the existence of copious amounts
of non-baryonic dark matter” and ”all of the proposed modifications of Big Bang nucleosynthesis
(BBN) appear to violate known observational constraints”. Similar concern is echoed by the authors
of the Report of the Dark Energy Task Force [5]. The report states: ”Dark energy appears to be
the dominant component of the physical Universe, yet there is no persuasive theoretical explanation
for its existence or magnitude. The acceleration of the Universe is, along with dark matter, the
observed phenomenon that most directly demonstrates that our theories of fundamental particles
and gravity are either incorrect or incomplete.”
In the following, we will explain how we may be able to explain the nucleosynthesis in a fundamental different way from that based on the Big Bang hypothesis.
∗ Corresponding

author: aribrynjolfsson@comcast.net

Ari Brynjolfsson: Nucleosynthesis in plasma-redshift cosmology

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We have previously shown [6-12] that the newly discovered plasma-redshift cross-section, which
follows from basic laws of physics, explains the redshifts of the solar Fraunhofer lines, the intrinsic
redshifts of stars, galaxies, and quasars, the cosmological redshifts, including the magnitude-redshift
relation for SNe Ia. The plasma redshift cross section also explains the cosmic microwave background
(CMB), and the X-ray background (see sections 5.10 and 5.11 and Appendix C of [6]). We have also
shown that the observed variations of surface brightness with the redshift confirm the predictions
of the plasma redshift, while contradicting the predictions of the Big Bang cosmology [12]. These
explanations, which are all based on the plasma-redshift cross-section have no need for expansion
of the universe, dark energy, or dark matter for explaining the observed phenomena. The failure to
deduce plasma redshift has also lead to failure to recognize the plasma-redshift heating of the solar
corona, galactic corona, and intergalactic plasma.
In light of plasma-redshift cross section, we find that contrary to general belief, the photons
are weightless in a local system of reference and gravitationally repelled as seen by an observer in
a distant system of reference. Photons’ weightlessness became clear when predictions of plasmaredshift theory were compared with the great many solar redshift experiments; see sections 5.1 to
5.6 of [6] and the theoretical explanation in [9]. The designs and the interpretations of the many
well-executed experiments that have been used in the past to prove the weight of the photon ignored
well-established laws of quantum mechanics [9] and made it impossible to see the weightlessness of
the photons. No conclusion about the photon’s weight could therefore be made [9].
Many consider the existence of ”black holes” (BHs) a proven fact. We refer to these objects as
”black hole candidates” (BHCs), because we consider BHs as hypothetical and not a proven fact;
see Narayan [13]. In plasma-redshift cosmology, the weightless hot photon ”bubbles” are formed at
the centers of BHCs during their collapse, as we will see. This prevents formations of BHs. The
very high temperatures at the centers of BHCs cause the nuclei in burned out star matter to fission
into primordial matter in accordance with conventional laws of physics.
The weightlessness of photons in the local system of reference is also important for explaining
the high temperatures in BHCs and the nucleosynthesis. Interestingly, together with the plasma
redshift cross section, the weightlessness of the photon (with gravitational mass mg = 0, while its
inertial mass as before is equal to mi = hν/c2 in the local system of reference) eliminates the need
for Einstein’s λ; that is, the world can be quasi static without Einstein’s λ.
For the readers unfamiliar with the plasma-redshift cosmology, we recap in section 2 some of the
main elements of it. In section 3, we discuss: a) why plasma-redshift cosmology has no black holes;
b) the collapsars; c) the super-massive black-hole candidates (SMBHCs) at the center of our Galaxy;
d) supernova SN 1987A; e) the diamagnetic moments and the jets from BHCs; and f) the gamma-ray
bursts. In section 4 we summarize the major conclusions.

2

Plasma redshift of photons

In addition to the cross sections for photo-electric effect, the Compton scattering, and the Raman
scattering, we have the plasma redshift cross section. This last mentioned interaction is important
only in hot sparse plasma. Photons energy loss through plasma redshift is in some aspects analogous
to the fast charged particles’ energy loss through Cherenkov radiation. In both cases the additional
energy loss is due to the dielectric constant. But there are also differences. Most of the fast charged
particles’ energy loss through Cherenkov radiation is emitted and reaches large distances, while
usually only a small fraction close to the interaction site is absorbed. In case of photons, the entire
plasma-redshift energy is quickly absorbed close to the interaction site. This absorbed energy, which
consists of very low energy quanta, results in significant heating of the plasma.
Plasma redshift of photons is also related to double and multiple Compton scattering of photons.
Regular Compton scattering consists of one incident photon and one scattered or outgoing photon;
but double and multiple Compton scatterings consist of one incident photon and two or more outgoing photons. When one of these outgoing photons’ frequency approaches zero, the cross section
approaches infinity. Heitler [14] thought that he had solved this so-called infrared problem. He estimated that the corresponding integrated product of the outgoing low-frequency photons’ energies

Ari Brynjolfsson: Nucleosynthesis in plasma-redshift cosmology

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and cross sections is small, or approximately 1/137 of the regular Compton cross section. This is
usually correct in ponderable matter, gasses, and in laboratory plasmas. But Heitler overlooked the
fact that when the incident photon penetrates very hot and very sparse plasmas, the very soft part
of the spectrum of the outgoing photon will interact simultaneously with great many electrons in
the plasma. The plasma redshift is about 50 % of the regular Compton cross-section multiplied by
the photon energy. We call this energy loss of the incident photons ”plasma redshift”, because it
occurs only in very hot and sparse plasma. The deduction of this plasma redshift and the necessary
conditions for plasma redshift are given in sections 1 to 4 and in Appendix A of [6]. The results of
the calculations are given by Eqs. (18) and (20) and Eq. (28) of that source, and are summarized in
Eqs. (1) and (2) below.

2.1

Predictions of plasma redshift

The plasma redshift is given by
ln(1 + z) = 3.326 · 10

−25

Z

R

Ne dx +
0

γi − γ0
,
ξω

(1)

where Ne is the electron density in cm−3 and x is in cm. γi is the initial quantum mechanical
photon width (half-width at half maximum in the Lorentz distribution for the line intensity. Lorentz
distribution is the same as the Breit-Wigner distribution in nuclear physics or Cauchy distribution
in mathematics). In the Sun, the Lorentzian form of the line dominates the Gaussian form of the
line beyond about three half-widths. This has been used for experimental determination of the
Lorentzian width of the solar photons.
The variations in the photon width, γi , are due to variations in both the intrinsic photon width
and the pressure broadening, which includes the Stark broadening. The classical photon width is
γ0 = 2e2 ω 2 /(3me c3 ) = 6.266 · 10−24 ω 2 ; where ω is the center frequency of the incident photon. For
the frequency range of main interest, we have that ξ ≈ 0.25.

2.2

The plasma-redshift cut-off

The plasma redshift is significant only when the plasma densities are low and the plasma temperatures high. This is the main reason why the plasma redshift was not discovered long time ago.
Plasma physicists were usually dealing with relatively dense and cold laboratory plasmas. Plasma
redshift is possible only if the following condition is fulfilled
2
T
5B
√e ˚
A,
(2)
λ ≤ λ0.5 = 318.5 · 1 + 1.3 · 10
Ne
Ne
Angstr¨om units, B is the magnetic field in
where λ is the wavelength of the incident photons in ˚
gauss units, Te is the electron temperature in degrees K, and Ne is the electron density in cm−3 .
Accordingly, the plasma redshift is not possible in conventional laboratory plasmas or in the reversing
layer and the chromosphere of the Sun, because the densities are too high and the temperatures too
low.

2.3

The cosmic microwave background

The cosmic microwave background (CMB) is emitted by the intergalactic plasma. According to
Eq. (1), the plasma-redshift absorption is κpl = 3.326·10−25 (Ne )av cm−1 . The absorption coefficient
is independent of the incident photon’s frequency as long as the frequency exceeds the cut-off given
by Eq. (2). From the observations of the supernovae Ia, we obtain Ne = 1.95 · 10−4 cm−3 . This
corresponds to one Hubble length LH = c/H0 = 1/κpl = 1.542 · 1028 cm ≈ 5, 000 Mpc.
The emission corresponding to the plasma-redshift absorption turns out to be the CMB. The
plasma-redshift absorption is more than million times greater than the conventionally used free-free
absorption at the CMB frequencies; see Appendix C of [6]. The dominance of the plasma-redshift
absorption explains the beautiful blackbody spectrum of the CMB.

Ari Brynjolfsson: Nucleosynthesis in plasma-redshift cosmology

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Within the blackbody cavity with a radius of LH = 1/κpl ≈ 5, 000 Mpc, the corresponding
blackbody radiation has a temperature obtained by equating in this case the radiation pressure with
the plasma pressure. We have (for details; see section 5.10 and Appendix C of [6])
4
a TCM
B = 3N kT,

or

TCM B =

3N kT
a

1/4
= 2.73 K,

(3)

where a = 7.566 · 10−15 dyne cm−2 K−4 is the Stefan-Boltzmann constant and k = 1.38 · 10−16 is the
Boltzmann constant. TCM B is the temperature of the CMB radiation. The value of TCM B = 2.73 K,
shown on the right side, is for N = Np + NHe++ + Ne = 1.917Ne and Ne = 1.95 · 10−4 cm−3 , and
T = 2.7 · 106 K. The value of Ne is obtained from the measurements of the magnitude-redshift
relation for supernovae SNe Ia. The good fit along the entire redshift range between the predicted
and the observed magnitude-redshift relation [6, 11] for supernovae supports the contention that the
density is correct, because otherwise the Compton scattering would cause the fits to deviate [6, 11].
The particle temperature T can be obtained independently from the measured X-ray background.
The CMB has a well-defined blackbody spectrum, because plasma-redshift absorption is about
106 to 1014 times greater than the usually used free-free absorption . The plasma-redshift absorption
determines the emission spectrum; see section C1.4 of Appendix C in [6].
The plasma around the galaxies and galaxy clusters have higher plasma densities and the product
of Ne T ≈ Ne Te is higher due to the gravitational attraction. The peak of the CMB spectrum shifts
therefore slightly towards higher temperatures in direction of clusters such as the great attractor.
This shift in the peak of the CMB is seen also in the direction of the Galactic center plane. This
perturbation from distant galaxies and galaxy clusters is rather small, because of the large Hubble
length, LH = 1/κpl ≈ 5, 000 Mpc, and limited angular resolution.

2.4

Weightlessness of photons

Most important for the explanation of the renewal of matter and many phenomena associated with
BHCs is the fact that the photons are weightless in a local system of reference (where the observer
and the photons are), but repelled in a reference system of distant observer, such as an observer
on Earth looking at photon experiments in the Sun or close to a BHC. This gravitational repulsion
of photons cancels the gravitational redshift, when the photons emitted in the Sun are observed on
Earth. This most remarkable discovery (because it contradicts general opinion) was made when the
predicted plasma redshift, based on the known electron densities and photon widths in the solar
corona, was compared with measured solar redshifts; see sections 5.6.1, 5.6.2 and 5.6.3, and Fig. (4)
in reference [6].
The weightlessness of photons is theoretically unrelated to the plasma redshift. But only when
comparing the observed solar redshifts with the theoretical predictions of the plasma redshift became
it clear that the solar redshifts, when observed on Earth, are not caused by Einstein’s gravitational
redshift. The great many other experiments that were believed to show that photons had weight
have, due to disregard for the uncertainty principle, all been interpreted incorrectly. The details of
the theoretical explanation of photons weightlessness are given in reference [9]. The weightlessness
of photons is a fundamental discovery that has great consequences for cosmology. It eliminates the
need for BH and Einstein’s Λ, it facilitates the explanation of the eternal renewal of matter, and it
modifies, but does not destroy, the theory of general relativity; see [9].

2.5

The conservation of energy

In plasma-redshift cosmology, the energy is conserved at all times. In Big Bang cosmology the energy
is not conserved. Instead, it may disappear into a black hole, or it may be created out of nothing in
form of a variable dark energy.
For illustrating the conservation of energy, let us consider a particle with mass m0 . At a large
distance from a BHC, its rest energy is Eo = mo c2 = hνo , where c is the velocity of light and
νo the frequency of the corresponding photon. When this particle falls, it transfers its change in

Ari Brynjolfsson: Nucleosynthesis in plasma-redshift cosmology

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gravitational potential energy, δE, to its surroundings in form of heat. The total rest energy of this
particle at the lower gravitational potential is then m c2g = ε mo (c/ε)2 = mo c2 /ε = hνo /ε = hν,
where ε = 1 + zg (see Møller’s Eq. (8.73) and Eq. 10.84 in [15]). When the redshifted photon returns
from the lower potential to the original position, its redshifted frequency and energy hν = hνo /ε
is reversed (blue shifted) resulting in energy equal to hνo to cancel the gravitational redshift. The
BHC (or the star) pushes the photon outwards. In doing so it returns the energy δE to the photon.
This shows that the energy is conserved in the present plasma-redshift theory. In the conventional
theory, the photons redshift is not reversed, and the energy is not conserved. This underscores the
beauty of the plasma-redshift cosmology.

2.6

Black holes in Big Bang cosmology

In the conventional Big Bang cosmology masses and all forms of energy have a gravitational mass. It
can then be shown that objects should be formed that are so massive that nothing can escape them,
not even light. These objects are called black holes (BHs). These bodies cannot emit blackbody
radiation and their blackbody temperature must be zero, as seen by a distant observer on Earth.
Nevertheless, the gravitational field and angular momentum is assumed to escape and affect surrounding objects. Principally, the time inside the BH can not be defined and the phenomena inside
the BH appear beyond the realm of classical physics. However, close to the BH limit, the quantum
mechanical uncertainty principle could play a role.
Stephen Hawking has conjectured that due to the uncertainty principle in quantum mechanics
some radiation could be emitted. This Hawking radiation from a black hole with a mass M has a
blackbody temperature given by
T =

¯hc3
M

K,
≈ 6.1 · 10−8
8πGM kB
M

(4)

where M
is the solar mass, kB the Boltzmann constant, G the gravitational constant, ¯h the Dirac
constant, and c the velocity of light. This equation shows that the temperature T is very low unless
the mass M is very small. The Hawking radiation has never been experimentally confirmed, nor has
the existence of a BH ever been confirmed.
According to Narayan [13], the black hole candidates (BHCs) are believed to have masses
M greater than 3M
to 5M
. X-ray binaries appear to have BHCs with masses on the order of 5M
to 10M
; and centers of galaxies are believed to have BHCs on the order of 106 to
109.5 times M
.

3

Nucleosynthesis in plasma-redshift cosmology

This section shows that when the mass of a collapsar increases beyond about 3 solar masses, the
collapsar does not form a BH, as usually conjectured. At the center, it forms instead a dense
weightless photon ”bubble” that prevents the formation of a black hole and facilitates primordial
like nucleosynthesis. The photon ”bubble” is surrounded by hot layers of quark-gluon plasma, then
hot neutron layers followed by layers of hot and dense proton-electron plasma.

3.1

No black holes in the plasma-redshift cosmology

In the general theory of relativity (GTR), the gravitational time dilation and the redshift are both
given by; see Møller’s Eqs. (8.114), (10.62) and (10.65) in [15]
dt = r
p

dτ
1−

2 G M/(R c2 )

− γι

2

uι /c

= ε dτ ,
−

(5)

u2 /c2

where the proper time τ is the time measured by an observer following the particle; and t is the
time measured by a distant observer far away from the gravitating body. ε = (1 + zgr ) is the GTR

Ari Brynjolfsson: Nucleosynthesis in plasma-redshift cosmology

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factor replacing the transversal Lorentz factor (1 − u2 /c2 )−1/2 in special theory of relativity (STR).
We have that
λgr
ε = (1 + zgr ) =
(6)
λ0
where zgr is the expanded gravitational redshift in Big Bang cosmology, which besides the usual
gravitational redshift includes modification by the particles movements, as given by Eq. (5).
When the reference system is not rotating, γι = 0, Eq. (5) takes the form
dt = p

dτ
1 − 2 G M/(R c2 ) − u2 /c2

(7)

−1

where G = 6.673 · 10−8 cm3 g s−2 is Newton’s gravitational constant. The mass M of the BHC is
defined from gravitational field when the radius R is large; and u is the velocity of the particle.
For u ≈ 0, this equation is valid for 2GM/(Rc2 ) < 1. Eq. (7) is then valid for
R > RS ≈

2GM
M
= 1.485 · 10−28 M = 2.95 · 105
cm .
c2
M

(8)

where RS , the Schwarzschild radius of the BHC. When R approaches this limit, the time increment,
dt, approaches infinity, and the frequency of light, the energy and the temperature approach zero.
Besides the velocities and thermal motions, electrical and magnetic fields can also affect the limit.
The limiting conditions for the different particles in the BHC have therefore a broad distribution.
The gravitational field affects not only time as in Eq. (5). At a point P the rest mass m = m0 ε,
the velocity of light c = c0 /ε, the frequency ν = ν0 /ε,, the photon energy hν = hν0 /ε, and the spatial
dimensions. The rest-mass energy, as seen by a distant observer, is given by mc2 = (m0 ε)(c0 /ε)2 =
m0 c20 /ε. The conservation of energy is valid at all times so that Ekin = (Ekin )0 /ε. We see thus that
Ekin = (Ekin )0 /ε = (m0 c20 − mc2 ) = m0 c20 (1 − 1/ε),

(9)

which for ε 1 is close to m0 c20 . In a local system of reference at rest at P, we have thus that
(Ekin )0 = εEkin = εm0 c20 − m0 c20 ,

(10)

which for large ε is much larger than the rest energy of the particle. Close to the center of the BHCs
the very hot matter will transform therefore into photons, which are weightless. This conclusion
does not require that ε = (1 + zgr ) is given by expressions in Eq. (5) and (7). This is important
because the concept of a point mass may not have a real physical meaning. In quantum mechanics,
the mass particle is always contained in a finite volume. Also, in plasma-redshift cosmology, the
photons weightlessness means that the gravitational mass is not conserved when the mass changes
to photons or photons change to mass. We have that the photon’s gravitational mass mg = 0, while
its inertial mass is mi = hν/c2 . The limiting radius of the BHC will often be inside the collapsar;
and it may therefore be difficult to define M and R. For interpreting Eqs. (9) and (10), we only
require that ε increases towards the center of the BHC.
The nuclear fusion, fission, and binding energies are insignificant, or less than 1 % of the rest-mass
energy. The initial heating close to the singularity is therefore about equal to the rest-mass energy.
All the equations in plasma-redshift cosmology are the same as the conventional equations. The
difference is only the weightlessness of photons, and the way the photon frequency varies when
the photon moves from the gravitating body (such as the Sun) outwards to a distant observer (for
example on the Earth). In plasma-redshift cosmology, the photon frequency increases and cancels
the gravitational redshift during the photon’s travel outwards (see section 2.6 above), while according
to Einstein’s GTR the photon’s gravitationally redshifted frequency stays constant as the photons
move outwards, for example, from the Sun to the Earth.
Had Einstein known that the photons are weightless, he would never have introduced his cosmological constant λ, because the photons weightlessness in the local system of reference (repulsion in
distant system of reference) eliminates the need for Einstein’s λ.

Ari Brynjolfsson: Nucleosynthesis in plasma-redshift cosmology

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The plasma-redshift cosmology accepts the conventional assumptions of physics, which demand
that the energy is conserved at all times, and that the time t in Eq. (5) is real at all times. Therefore,
in plasma-redshift cosmology we cannot have a black hole. Eqs. (9) and (10) show how the plasmaredshift cosmology can easily deny the existence of a black hole. From Eq. (8) we get that the average
gravitational mass density ρg within a sphere with radius R must at all times in the local system of
reference meet the condition that
ρg · R2 < 1.6076 · 1027 g cm−1 .

(11)

When the product ρg · R2 approaches the limit 1.6076 · 1027 , at least some of the gravitational mass
must convert into weightless photons. This prevents formation of a BH. Eq. (11) must be valid
throughout the universe. On the other hand, in the Big Bang cosmology, the value of ρg · R2 may
be equal to or exceed this limit, which results in a BH.
Important is also the fact that when a particle with rest mass m0 moves from infinity to the surface
of a BHC, the kinetic energy gained is not equivalent to the potential energy difference between the
infinity and the surface, as usually believed. Instead, the total gain in kinetic energy is about equal
to the particle’s rest-energy m0 c2 . It is as if the particle had fallen all the way to the brink of a
BH. This correction of the conventional calculations is important, because it significantly increases
the heating at the center of the BHC. This rule applies to collapsars with the hot photon bubbles
at their centers. The weight of the particle at the surface will squeeze the mass of the collapsar
to release, mostly close to the center of the BHC, a total energy close to m0 c2 . The accretion of
matter may easily lead to growth of the BHC to SMBHCs.
Before any large mass unit, such as an iron nucleus, transforms into photon energy, it usually will
fission into hadrons, such as protons and neutrons, which in turn may fission into the fundamental
particles, such as the quarks, the antiquarks, and the leptons (which include electrons (e), muons
(µ), and tau particles (τ , ) and their antiparticles and the corresponding neutrinos), and the bosons
(which include photons, gluons, Z-bosons, and W-bosons). The fission and fusion energies of nuclei
amount to a small fraction of the rest-mass energy, or usually less than about 1 %.
This is consistent with experiments, such as the Relativistic Heavy Ion Collider (RHIC) experiments at Brookhaven National Laboratory; see Shuryak [16]. The deconfinement of the quark matter
occurs at temperature on the order of 170 MeV [16, 17, 18], or at about 192 MeV, as some other
estimates indicate, see Cheng [19]. The transformations and heating will absorb most of the energy,
which in the conventional Big Bang theory was assumed to disappear into the black hole.
This hot quark-gluon plasma emits weightless photons [20, 21, 22, 23, 24, 25, 26]. The quarks
and the leptons are fermions and are therefore governed by the Pauli exclusion principle. Identical
fermions are pushed apart and therefore outwards. The photons, which are bosons, are not governed
by the exclusion principle. They will then separate from the fermions and be squeezed inwards and
concentrate at the center of the BHC. The gluons, Z-bosons, and W-bosons usually stay close to the
quarks and the leptons. The weightless photons at the center of the BHC eliminate the black hole
singularity in Eq. (5), because at the surface of the photon bubble the gravitational attraction is zero.

3.2

Collapsars

A large, burned out star will reach a point when the thermal pressure of the particles can no longer
balance the gravitational attraction. The star will then shrink. However, even when all fusions cease,
the exchange interactions between the identical fermions often can counter balance the gravitational
attraction. Initially, the electrons (having the smallest mass) set the limit and prevent the collapse
if the star mass M is less than about 1.4 M
, the maximum mass for a white dwarf. If M increases
beyond this limit, the star collapses further to a neutron star. In turn, the exchange interactions
between the neutrons cannot prevent a collapse to a BHC if the mass exceeds about M ≈ 2.5 M
.
The Big Bang cosmologists assume therefore that the BH do exist, because the physical laws, as
they know them, can’t circumvent their formation.
In the plasma-redshift cosmology, on the other hand, the formation of the BH can be circumvented,
as we saw in previous section. When the collapsar is large enough to form a BHC, the temperature
at its center is high enough to transform the mass into photons. The exchange interactions, which

Ari Brynjolfsson: Nucleosynthesis in plasma-redshift cosmology

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involve identical fermions in the quark-gluon plasma layer and in the neutron layer, push the the
fermions outwards, and squeeze thereby the photons (which are unaffected by the exchange forces)
inwards. The weightless photons, which are bosons, collect therefore at the center of the BHC and
prevent thereby the formation of the BH. The physics for collapsar below the mass limit for BHC is
in plasma-redshift cosmology nearly identical to the physics in conventional Big Bang cosmology. We
can then in plasma-reshift cosmology use the conventional models that have been used to describe
the neutron stars and pulsars in Big Bang cosmology.
For example, for a non-rotating neutron star with mass M ≈ 1.4 M
, we can use the equation
of state assumed by Akmal et al. [27], as modified by Olson [28], or by Kratstev and Sammarruca
[29]. A neutron star with density equal to the normal nuclear energy density, which is about
153 MeV fm−3 or 2.73 · 1014 g cm−3 , would have a partial (along each axis) pressures of about
px = 1.27·1033 dyne cm−2 . The energy density at the center of a 1.4 M
star with radius of about 12.7
km will be about 317 MeV fm−3 , corresponding to a mass density at the center of 5.65 · 1014 g cm−3 .
The corresponding partial pressure at the center would be px = 2.44 · 1034 dyne cm−2 ; see [28].
Akmal et al. [27] believe, based on laboratory experiments, that the neutron star becomes unstable when its mass increases and approaches M ≈ 2.2 M
. They set an upper limit of M ≈ 2.5 M
.
Laboratory experiments make it likely that at the centers of such stars, matter transforms to quarkgluon plasma [29]. These predictions are crude but consistent with observations [29, 30, 31, 32]. They
are also consistent with plasma-redshift cosmology, because we may have that in the transition zone
1.8 M
≤ M ≤ 2.5 M
, a quark-gluon plasma is formed that emits and transforms into photons,
which form a bubble that prevents any part of the star from reaching the black-hole limit. A small
bubble has only a small effect on the conventional equations of state.
The state will depend on the rotation. For a crude overview, we may use as a guide the models
for ”Fast rotation of strange stars” developed by Gourgoulhon et al. [33]. From their estimates and
their figures 2 and 4, it is clear that the star stretches in the equatorial direction as the rotation
increases. When the surface at the equator exceeds the limit for bound orbit, the star loses mass at
the equator. Such a BHC may accrete mass and the bubble at the center will grow. The bouncing
back and forth across the bubble gradually reduces the angular momentum, and the BHC may grow
into a slowly rotating super-massive BHC (SMBHC).
The photons being bosons can be compressed at will. The photon bubble, which following the
initial collapse is heavily compressed, will therefore bounce back. Some of the energy can result in a
supernova eruption, some of it may be released in form of primordial plasma and some in a gammaray burst, confer SN 1987 A. Most important change from conventional physics is that collapsar will
have a hot photon bubble at its center, which is surrounded by quark-gluon plasma, then neutron
layers, and proton-electron plasma layers. The transition between the different layers is gradual; for
example, mainly the outer layers of the photon bubble will be mixed with quark-gluon plasma.

3.3

SMBHC at the center of our Milky Way

Every galaxy is believed to contain a supermassive black hole candidate (SMBHC) with a mass often
in the range of 106 to 3 · 109 solar masses. In our Galaxy the SMBHC in Sgr A∗ with mass of about
M ≈ 3.7 · 106 M
has been exceptionally well studied [34 - 42].
With help of inflation, dark energy, and dark matter many phenomena appear to confirm to
the expectations of the Big Bang cosmologists. One of the phenomena that has been difficult to
understand is the youth of the stars, such as, O8-B0 main sequence stars with masses of about 15 M

and ages less than 10 million years, in the immediate surroundings of the SMBHC [34, 35, 42].
Plasma-redshift cosmology indicates that BHCs and SMBHCs are very hot. The density in the
photon bubble and in the surrounding quark-gluon plasma decreases as the BHCs grow. But the
temperature in the photon bubble at the center surrounded by quark-gluon plasma will still be
very high, and will exceed about 192 MeV, or 2.2 · 1012 K. Outside the quark-gluon plasma and
the neutron layers, the electron-proton plasma is also very hot. In the inner layers all the heavier
nuclei will have fissioned into protons and neutrons. The temperature of the outer layers decreases
gradually. When the temperature decreases below about 15 MeV in the outer layers, some fusion
can take place; first, with formation of helium and then lighter elements. Different disturbances can

Ari Brynjolfsson: Nucleosynthesis in plasma-redshift cosmology

9

lead to release of high density primordial matter from the SMBHC at the center of our Galaxy. Such
matter can result in star formation close to the Galactic center. Plasma redshift gives thus a natural
physical explanation of the observations of youthful stars at the center of our Galaxy. Interestingly,
the very high temperatures and densities in some of the layers of the SMBHC may lead to spallation
and to formation of 6 Li and other isotopes that Big Bang scenario had difficulties in explaining.
The observed dimness and infrared emission from the SMBHC at the Galactic center has also
been difficult to explain; see [34 - 38].
In plasma-redshift cosmology, the plasma-redshift cross-section dominates the absorption and
emission processes in the very hot coronal like plasma surrounding the SMBHCs. The black body
emission temperature, Tbbem , from the fully ionized plasma around a SMBHC is given by Eq. (3) or
4
a Tbbem
= 3N kT = 5.75Ne kT K,

(12)

where a = 4σ/c = 7.566·10−15 dyne cm−2 K−4 is the Stefan-Boltzmann constant and k = 1.38·10−16
is the Boltzmann constant, and N ≈ 1.917Ne . In the outermost corona, the densities may be
Ne ≈ 4.6 · 104 cm−3 and the particle temperature T ≈ 2 · 106 K. The emission temperature is then
Tbbem ≈ 100 K. For Ne ≈ 4.6 · 106 cm−3 and the particle temperature T ≈ 4.4 · 107 K. The emission
temperature is then Tbbem ≈ 1000 K. If the emission areas have a radius of about 7.5 · 1015 cm
and 7.5 · 1013 cm, respectively, the emitted energy would be about 1036 erg s−1 , as observed. These
outer reaches of the corona are transparent to optical light. The limb effect and the variation of
Ne and T with depth complicate the estimates. In addition, we must take into account synchrotron
radiation, which increases the luminosity at frequencies around ν ≤ 1012 s−1 . These examples serve
therefore only as rough indicators. Without going into elaborate details, however, they indicate
that the plasma-redshift cross-section can explain the observed low-energy emission, which is about
1036 erg s−1 .
In Big Bang cosmology, it is often assumed that the BHCs and the SMBHCs are relatively cold
(mainly because the hot matter and energy are sucked into the BH). The low emission is often
explained as due to low surface temperature. It was difficult therefore to explain the large X-ray
flares often observed.
Plasma-redshift cross-section dominates in the sparse outer layers of the corona. But in the deeper
and denser corona the free-free emission and absorption may dominate at the higher temperatures
and higher (X-ray) frequencies, because plasma redshift is proportional to Ne , while the free-free
emission is proportional to Ne2 . Just like in the Sun we often have eruptions usually initiated (like
in the Sun) by a strong magnetic fields which lower the plasma redshift cut-off frequencies, see
Eq. (2). The cut-off region for these frequencies may then penetrate deep into the corona. Once the
additional plasma redshift heating starts in these deep layers, the conversion of magnetic field energy
to heat kicks in and augments the plasma-redshift heating and makes it explosive. (The physics of
the solar flares are described in section 5.5 of reference [6], and the relevant free-free emissions and
absorptions in Appendix C1 and C2 of that source.) Plasma-redshift cross-section gives thus a
rather simple explanation of these difficult to explain observations of X-ray flares.
The observations of the Galactic center are consistent with a SMBHC with a hot (about 192 MeV,
or 2.2 · 1012 K) photon bubble at its center, which is is surrounded by quark-gluon plasma, neutron
layers, and layers of electron-proton plasma corona, as predicted by the plasma-redshift cosmology.
In the deeper layers of the SMBHC the temperature is so high that no heavy nuclei exist. Instead,
we have a large reservoir of primordial matter at the center of the SMBH.

3.4

SN 1987 A

The excellent phenomenological descriptions of the collapse of Sanduleak −69◦ 202, a B3 I star, to
form SN 1987A in a Type II core-collapse explosion show many phenomena that are at odds with
that expected, as pointed out by Panagia [43], who is one of those that has studied this subject
thoroughly. He writes: ”The early evolution of SN 1987A has been highly unusual and completely
at variance with the wisest expectations.”
The collapse of such a large star, M ≈ 20 M
, was expected to result in a BH, but we see no
indication of that. But the plasma-redshift cosmology gives a natural explanation. It suggests that

Ari Brynjolfsson: Nucleosynthesis in plasma-redshift cosmology

10

before the limit of BH is reached, the matter transforms into weightless photons at the center of the
collapsar. These weightless photons prevent formation of a BH.
The collapsed SN 1987 A showed very fast brightening (within one day) and the fast decay of that
ultraviolet flux; but no good physical explanation could be given
But in plasma-redshift cosmology a huge pulse of brightness must follow immediately after the
collapse. A star with mass of M ≈ 20 M
, will during the collapse release at the center of the
collapsar a large fraction of the gravitational potential energy in form of a thermal energy. A fraction
of that energy transforms into photons that form a hot bubble at the center of the collapsar. Due
to the fast rotation, the bubble will be thrown outwards and form a torus close to the periphery
of a flattened disk. The photons may concentrate in one or more swellings along the torus. Due
to rotational stresses, the enclosure around the torus is likely to burst and release some of the
high-energy photons. These photons will interact with the quark-gluon plasma, the neutrons, and
the proton-electron plasma on their way out and release hot primordial matter together with the
high energy photons. This sudden release of primordial matter and intense high-energy photons
will fall-off fast, as the pressure in the bubble decreases. The relatively short pulse of high-energy
photons interacts with circum-stellar matter by producing huge amounts of electron-positron pairs,
which also contribute to the ionization and excitation of the circum-stellar matter. This produces
the light echoes and rings as suggested by Panagia [43].
Why the low luminosity following the relaxation of the initial brightness? Some of the primordial
matter that gushes out will cover up the collapsar with hot electron-proton plasma. The Compton
scattering and absorption in this hot and dense electron-proton plasma reflects and absorbs the high
energy radiation from inside the collapsar. When relaxed after the initial pulse, the outer most
layers of the plasma will cover up the BHC, and will emit infrared radiation that thermally insulates
the BHC; see Eq. (12) in subsection 3.3. This equation explains why the luminosity is many orders
of magnitude smaller than that from a hot excited atomic and molecular matter. We often see
reference to barium and nickel lines emitted from the collapsar. I believe that these lines are from
the pre-collapse surroundings and not from the proper collapsar, which consists mainly of primordial
and youthful matter.
How were the rings formed? Usually, it is assumed that the inner and outer rings are left over
debris from explosions in the blue giant when it was a red giant. In the plasma-redshift cosmology
this may be a correct explanation, but a modification of this conventional explanation may also be
possible.
Plasma-redshift cosmology shows that all stars must have a corona. Plasma-redshift initially
transfers the energy loss of photons to the electrons [6], which then ionize the atoms. The sphere of
ionization stretch far beyond the conventionally estimated Str¨omgren radii. All stars have plasma
spheres analogous to the heliosphere. The radius of the heliopause is on the order of 2.2 · 1015
cm; see Fig. 5 of Opher et al. [44]. Plasma-redshift heating causes the radius of the plasma sphere
around stars to increase with their luminosity. Sanduleak-690 202 had a luminosity of L ≥ 105 L
,
see Nathan Smith [45]. For interstellar densities and magnetic fields similar to √that in the solar
neighborhood, we expect the radius of the star’s plasma sphere to be in excess of 105 = 316 times
that of the Sun, or in excess of about 7 · 1017 cm. The radius to the colder and denser layers outside
the plasma sphere is likely to be about 1.3 to 1.6 · 1018 cm, which is about equal to the distance to
the outer rings of SN 1987, as determined by Panagia [43]. Many other factors affect the estimated
radius, such as the direction and intensity of the magnetic field, the density and pressure of the
interstellar matter, and the motion of the star relative to the interstellar medium. This is therefore
a crude estimate. It merely makes the formation of the matter around SN 1987-690 202 reasonable
without any particular explosions.
Plasma redshifts initiates large flares in the Sun [6]. Similar flares are likely to be initiated,
especially in large stars like B3 Ia star Sanduleak 690 202. These flares carry large amount of matter
into the far reaches of the corona, especially, along the center plane of the rotation. This may explain
the inner ring.
Very intense high-energy photon beams will stream out through holes or ruptures in the swellings
on the torus at the end of the collapse. The torus is unlikely to be uniform with photon bubbles
concentrating in swellings at one or more places. Due to the centrifugal forces, the torus is likely

Ari Brynjolfsson: Nucleosynthesis in plasma-redshift cosmology

11

to rupture a few places, especially in the equatorial plane, but it may also rupture at one or more
places along the ridge of the torus. The fast rotation will spray a beam in a circle. This is suggested
only as a possible explanation of the ring formation.
The rings may diffuse and cool down and become dust rings, as confirmed by Bouchet et al. [46].
Most of the very high-energy photons and high energy particles released in the initial flash were
not (and due to lack of proper instrumentation could not be) detected. The low grain temperature,
about 166 K, observed by Bouchet et al. [46] does not conflict with the much higher, about 2 · 106
K, temperature in line forming elements observed by Gr¨oningsson et al. [47].
We see thus that plasma-redshift cosmology gives a reasonable physical explanations of many of
the phenomena around SN 187 A. Many of these phenomena could not be easily explained in the Big
Bang cosmology.

3.5

Diamagnetic moments and plasma jets from BHCs

In plasmas, the diamagnetic moments created by the charged particles encircling magnetic field lines
are strongly coupled and oppose the magnetic field. On the average, the energy density of the field
is about equal to the kinetic energy density of charged particles. When the magnetic field moves
with the plasma from hotter region to a colder region, the energy density of the field usually exceeds
the kinetic energy density of the particles. The plasma-redshift heating reverts then the magnetic
field energy to heat, just as it does in the solar atmosphere; see subsection 5.5 and Appendix B of
[6]. In and above the photosphere this energy conversion may cause solar flares like eruptions and
hot bubbles.
Plasma-redshift together with the magnetic field thus creates hot bubbles with denser plasma (or
even ”clouds”), on the surface of these hot bubbles. The dense plasma may leak due to gravitation
into the SMBHC, just as high velocity clouds leak into the Galaxy [6]. In the solar corona, we also
have plasma-redshift heating push matter into arches. The condensed plasma leaks down both ends
of these arches back into the Sun. These processes are the main source of accretion onto SMBHC.
Divergence in the magnetic field accelerates the charged particles outwards. In Appendix B of
[6], we show (see Eq. B9 of [6]) that the force, FP , on a charged particle at a point P is given by
FP =

n m vP2
,
2 RP

(13)

which is independent of the magnetic field strength. The particle’s velocity, v⊥ , at right angle to
the field is given by
BP
2
v⊥
= vP2
,
(14)
B
where the magnetic field B at the point P decreases outwards as
n
RP
B = BP
,
(15)
R
The force given by Eq. (13) pushes the diamagnetic dipole of the charged particles outwards. Especially in the very hot plasma around the BHC, the value of vP2 may exceed GM/Rc , where Rc
is the distance of the point P from the gravitational center, and M is the gravitational mass inside
P . The force FP pushing the diamagnetic moment outwards may therefore exceed the gravitational
attraction. The energy gained can exceed 1020 eV. We find it likely that this accounts for the fast
jets often seen being pushed outwards from BHC. It may even account for the highest energy cosmic
rays. These jets are fed mainly by the hot proton-electron plasma surrounding the BHC. Plasmaredshift cosmology thus gives a natural physical explanation of the jets seen streaming away from
many BHC and SMBHC.

3.6

Gamma-ray bursts

As we have seen, the photon bubbles in large BHCs come in many sizes. Many triggers, such as
passage of a star close the BHCs, can initiate an outburst. When the fragile containment opens up

Ari Brynjolfsson: Nucleosynthesis in plasma-redshift cosmology

12

and releases the photons from the center, the photons may not have time to react with the quarkgluon plasma, the neutron layers, or the electron-proton plasma surrounding the BHC. A BHC may
then suddenly release photons equivalent to a small fraction or a large number of solar masses. Such
gamma-ray bursts therefore come in many sizes. A quiescent SMBHC at the center of our Galaxy
releases the primordial matter and the photons usually in smaller bursts. Initially, the high energy
photons interact with matter mainly by producing electron-positron pairs. The characteristic 511
keV annihilation line observed mainly in the galactic center is a clear indicator of this. The often
surmised positron decay of isotopes seem inadequate for explaining the large intensities reported by
Weidenspointner et al. [49]. Without the present plasma-redshift cosmology, it is difficult to explain
the observations. This appears to be still another confirmation of plasma-redshift cosmology.

4

Summary and conclusions

The plasma-redshift cross section is not hypothetical, as it is derived theoretically from conventional
laws of physics without any new assumptions. It explains great many cosmological phenomena that
in the conventional Big Bang cosmology defied physical explanations.
1. Plasma redshift explains the solar redshift, the cosmological redshift, and why all stars, galaxies
and quasars have intrinsic redshifts, due to the fact that when a photon penetrates a hot
sparse plasma, it is redshifted in accordance with Eq. (1) and (2) ; see the deduction in [6].
Plasma redshift also explains the heating of the solar corona, the galactic coronas, and the
intergalactic space. The energy the photons lose in the plasma redshift is absorbed in the
plasma and transformed into heat [6].
2. The cosmological redshift is not due to expansion as assumed in the Big Bang cosmology, but to
plasma redshift of photons in intergalactic plasma with average temperature of 2.7 · 106 K, and
electron density of 2 · 10−4 cm−3 . Plasma redshift explains the observed magnitude-redshift
relation for supernovae Ia without any expansion, dark energy, or dark matter [6, 7, 11, 12].
3. Big Bang cosmology assumes cosmic time dilation. Perusal of the experiments, which were
thought to prove cosmic time dilation, shows that the proofs are invalid [6, 7, 11]. Consistent
with all observations, the plasma-redshift theory shows that there is no cosmic time dilation.
4. According to the Big Bang cosmology, the cosmic microwave background (CMB) originated in
a plasma at a redshift of about z = 1400 [1]. In contrast to this, plasma-redshift cosmology
explains that the CMB with its beautiful blackbody spectrum is emitted from the intergalactic
hot plasma without any expansion; see subsection 5.10 of [6]. The required average density
and average temperature are exactly the same as those required to explain the cosmological
redshift and the X-ray background; see subsection 5.11 and Appendix C of [6].
5. In the Big Bang cosmology, we cannot explain the X-ray background, because the intergalactic
space is assumed cold and practically empty. In plasma-redshift cosmology, the observed X-ray
background follows from the same densities and temperatures of the intergalactic plasma as
those needed to explain the cosmological redshift and the microwave background radiation;
see subsection 5.11 of [6].
6. Scrutiny of solar experiments shows that most of the redshifts, when observed on Earth, are
not due to the gravitational redshifts, but are due to the plasma redshifts given by Eq. (1) and
(2); see [6] and [9].
7. The experiments in laboratories and in space that have been assumed to prove photons gravitational redshift did not allow adequate time for the change in photons frequency. Heisenberg
uncertainty principle shows that the time difference between emission and absorption of the
photons was too small for the given potential difference. The experiments were therefore incorrectly designed and the observations incorrectly interpreted [9]. The plasma redshift shows
clearly that the photons redshift is reversed when they move from the Sun to the Earth [6].

Ari Brynjolfsson: Nucleosynthesis in plasma-redshift cosmology

13

This reversal of the gravitational redshift means that the photons are weightless in the local
system of reference, but repelled by the gravitational field in the reference system of a distant
observer; see [9].
8. The weightlessness of photons shows that Einstein’s equivalence principle is wrong [9]. The
gravitational mass, mg = 0, of a photon is not equivalent to its inertial mass, mi = hν/c2 . The
enormity of this finding for gravitational theory should be appreciated. Presently, we modify
the equivalence principle to apply always, except to photons (possibly to all elementary bosons).
9. When a mass particle approaches the BH limit of a BHC or a SMBHC, its kinetic energy, in
the local system of reference (see Eq. 10), may exceed significantly its rest mass energy. Mass
then converts to photons that accumulate at the center of the collapsar due to repulsive forces
on the fermions. The weightless photons at the center prevent the formation of a BH.
10. Time is described with a real number everywhere and at all times, because there are no black
holes; see subsection 3.1. The problem of ever-increasing time and ever-increasing entropy is
resolved when we realize that we are usually observing only one half of the material-photon
cycle. We usually focus on the physical changes from creation of matter through its changes
(which define the time) towards burned out stars and their transformation in large BHCs,
while often disregarding the other half of the time cycle; the creation of photons and their
transformation to matter in an ever lasting renewal process.
11. Although the universe is quasi-static, infinite and ever lasting there is no Olbers’ paradox. The
reduction of the light intensity in the plasma-redshift absorption resolves this problem; see [6].
12. In the Big Bang cosmology, the stars will run out of energy and will have a finite lifetime.
Plasma-redshift cosmology by contrast leads to eternal renewal of matter and stars, as we
have seen in this article. The plasma-redshift cosmology leads to transformation of burned
out matter to photon bubbles at the centers of BHCs and SMBHCs. The hot photon bubbles
and the hot centers of BHCs and SMBHCs lead to renewal or recreation of primordial matter.
This primordial matter leads to the nucleosynthesis and to formation of new stars for ever.
We have demonstrated that plasma redshift, which is based on fundamental and basic conventional physics without any new or additional assumptions, leads by necessity to renewal of matter
in BHC and thereby to fundamental changes in our cosmological perspective.